#!/usr/bin/env python

# In the 20 x 20 grid below, four numbers along a diagonal line have been
# marked in red.

# 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
# 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
# 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
# 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
# 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
# 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
# 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
# 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
# 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
# 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
# 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
# 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
# 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
# 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
# 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
# 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
# 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
# 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
# 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
# 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48

# The product of these numbers is 26  63  78  14 = 1788696.
# What is the greatest product of four adjacent numbers in any
# direction (up, down, left, right, or diagonally) in
# the 20 x 20 grid?

import operator

from python.decorators import euler_timer
from python.functions import get_data

def make_path(point, step, length):
    return [(point[0] + i*step[0], point[1] + i*step[1]) for i in range(length)]

def convert(path, data):
    # Assumes path is made of points (x,y) where data[x][y] exists
    return reduce(operator.mul, [data[x][y] for x, y in path])

def main(verbose=False):
    DATA = get_data(11)
    DATA = [[int(entry) for entry in row.split()]
            for row in DATA.split("\n") if row]

    # UP/DOWN goes from DATA[x][y] to DATA[x+3][y] where 0 <= x, x+3, y <= 19
    vert = max(convert(make_path((x, y), (1, 0), 4), DATA) for x
               in range(0, 16 + 1) for y in range(19 + 1))

    # LEFT/RIGHT goes from DATA[x][y] to DATA[x][y+3] where 0 <= x, y, y+3 <= 19
    horiz = max(convert(make_path((x, y), (0, 1), 4), DATA) for x
                in range(0, 19 + 1) for y in range(16 + 1))

    # DIAGONAL L->R goes from DATA[x][y] to DATA[x+3][y+3] via +[1,1]
    diag_l_r = max(convert(make_path((x, y), (1, 1), 4), DATA) for x
                   in range(0, 16 + 1) for y in range(16 + 1))

    # DIAGONAL R->L goes from DATA[x][y] to DATA[x-3][y+3] via +[-1,1]
    diag_r_l = max(convert(make_path((x, y), (-1, 1), 4), DATA) for x
                   in range(3, 19 + 1) for y in range(16 + 1))

    return max(vert, horiz, diag_l_r, diag_r_l)

if __name__ == '__main__':
    print euler_timer(11)(main)(verbose=True)
